After picking the design, many calculations needed to be done. After the curvature of the dome was taken into consideration, there would be five different strut lengths.
At a later date, I plan on doing a write up on the geometry involved with these next few steps, but right now it is beyond the scope of this page.
Mathematically, the dome was built inside a sphere of radius 1, (units are not important at this point, it can be one inch or one kilometer). Inside this sphere, the lengths of the five different struts were calculated. Since no strut is longer than the radius all numbers were smaller than one. These numbers are known as "cord factors". Multiplying a cord factor by a desired dome radius gives the strut lengths for each piece. This way, any changes in the dome size can be easily calculated.
Using the cord factors, I built an Excel spreadsheet. The first cell allows you to put in the radius of the dome. It would then calculate the lengths of all the struts.
| Dome Radius in Inches | |||||
| 171 | |||||
| Strut-A | Strut-B | Strut-C | Strut-D | Strut-E | |
| Cord Factors | 0.3486 | 0.2865 | 0.2028 | 0.3628 | 0.4124 |
| Length of Struts between Center of Pins (inches) | 59.61 | 48.99 | 34.68 | 62.04 | 70.52 |
| TOTAL LENGTH of STRUTS With extra 1.5" for bolt holes | 61.11 | 50.49 | 36.18 | 63.54 | 72.02 |
| Hole placements before bend (pin length plus 1/16") | 59.74 | 49.12 | 34.80 | 62.16 | 70.65 |
| Distance from center of hole to fold (inches) | 3.47 | 3.47 | 3.47 | 3.47 | 3.47 |
| Tangent Angle (degrees) | 10.04 | 10.45 | 11.90 | 8.24 | 5.82 |
| Number of Pieces | 32 | 32 | 92 | 58 | 54 |
| Length of Material (feet) | 162.96 | 134.64 | 277.37 | 307.10 | 324.09 |
| Total Number of Struts | 268 | ||||
| Total Length of Struts (Feet) | 1206.17 | ||||
| Weight of Dome (pounds) | 1055 | ||||